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Understanding the structure of multidimensional patterns, especially in unsupervised cases, is of fundamental importance in data mining, pattern recognition, and machine learning. Several algorithms have been proposed to analyze the structure of high-dimensional data based on the notion of manifold/earning. These algorithms have been used to extract the intrinsic characteristics of different types of high-dimensional data by performing nonlinear dimensionality reduction. Most of these algorithms operate in a "batch" mode and cannot be efficiently applied when data are collected sequentially. In this paper, we describe an incremental version of ISOMAP, one of the key manifold learning algorithms. Our experiments on synthetic data as well as real world images demonstrate that our modified algorithm can maintain an accurate low-dimensional representation of the data in an efficient manner. [ABSTRACT FROM AUTHOR]

The scalability problem in data mining involves the development of methods for handling large databases with limited computational resources such as memory and computation time. In this paper, two scalable clustering algorithms, bEMADS and gEMADS, are presented based on the Gaussian mixture model. Both summarize data into subclusters and then generate Gaussian mixtures from their data summaries. Their core algorithm, EMADS, is defined on data summaries and approximates the aggregate behavior of each subcluster of data under the Gaussian mixture model. EMADS is provably convergent. Experimental results substantiate that both algorithms can run several orders of magnitude faster than expectation-maximization with little loss of accuracy. [ABSTRACT FROM AUTHOR]

This paper proposes a k-means type clustering algorithm that can automatically calculate variable weights. A new step is introduced to the k-means clustering process to iteratively update variable weights based on the current partition of data and a formula for weight calculation is proposed. The convergency theorem of the new clustering process is given. The variable weights produced by the algorithm measure the importance of variables in clustering and can be used in variable selection in data mining applications where large and complex real data are often involved. Experimental results on both synthetic and real data have shown that the new algorithm outperformed the standard k-means type algorithms in recovering clusters in data. [ABSTRACT FROM AUTHOR]